SRC/dsbgvd.f(3)

NAME
SRC/dsbgvd.f

SYNOPSIS

  Functions/Subroutines
subroutine dsbgvd (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, lwork, iwork, liwork, info)
DSBGVD

Function/Subroutine Documentation

  subroutine dsbgvd (character jobz, character uplo, integer n, integer ka, integer kb, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( ldbb, * ) bb, integer ldbb, double precision, dimension( * ) w, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer info)

DSBGVD

Purpose:

    !>
    !> DSBGVD computes all the eigenvalues, and optionally, the eigenvectors
    !> of a real generalized symmetric-definite banded eigenproblem, of the
    !> form A*x=(lambda)*B*x.  Here A and B are assumed to be symmetric and
    !> banded, and B is also positive definite.  If eigenvectors are
    !> desired, it uses a divide and conquer algorithm.
    !>
    !>

Parameters
    JOBZ

    !>          JOBZ is CHARACTER*1
    !>          = 'N':  Compute eigenvalues only;
    !>          = 'V':  Compute eigenvalues and eigenvectors.
    !>

    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangles of A and B are stored;
    !>          = 'L':  Lower triangles of A and B are stored.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrices A and B.  N >= 0.
    !>

    KA

    !>          KA is INTEGER
    !>          The number of superdiagonals of the matrix A if UPLO = 'U',
    !>          or the number of subdiagonals if UPLO = 'L'.  KA >= 0.
    !>

    KB

    !>          KB is INTEGER
    !>          The number of superdiagonals of the matrix B if UPLO = 'U',
    !>          or the number of subdiagonals if UPLO = 'L'.  KB >= 0.
    !>

    AB

    !>          AB is DOUBLE PRECISION array, dimension (LDAB, N)
    !>          On entry, the upper or lower triangle of the symmetric band
    !>          matrix A, stored in the first ka+1 rows of the array.  The
    !>          j-th column of A is stored in the j-th column of the array AB
    !>          as follows:
    !>          if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
    !>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka).
    !>
    !>          On exit, the contents of AB are destroyed.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= KA+1.
    !>

    BB

    !>          BB is DOUBLE PRECISION array, dimension (LDBB, N)
    !>          On entry, the upper or lower triangle of the symmetric band
    !>          matrix B, stored in the first kb+1 rows of the array.  The
    !>          j-th column of B is stored in the j-th column of the array BB
    !>          as follows:
    !>          if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
    !>          if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb).
    !>
    !>          On exit, the factor S from the split Cholesky factorization
    !>          B = S**T*S, as returned by DPBSTF.
    !>

    LDBB

    !>          LDBB is INTEGER
    !>          The leading dimension of the array BB.  LDBB >= KB+1.
    !>

    W

    !>          W is DOUBLE PRECISION array, dimension (N)
    !>          If INFO = 0, the eigenvalues in ascending order.
    !>

    Z

    !>          Z is DOUBLE PRECISION array, dimension (LDZ, N)
    !>          If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
    !>          eigenvectors, with the i-th column of Z holding the
    !>          eigenvector associated with W(i).  The eigenvectors are
    !>          normalized so Z**T*B*Z = I.
    !>          If JOBZ = 'N', then Z is not referenced.
    !>

    LDZ

    !>          LDZ is INTEGER
    !>          The leading dimension of the array Z.  LDZ >= 1, and if
    !>          JOBZ = 'V', LDZ >= max(1,N).
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK.
    !>          If N <= 1,               LWORK >= 1.
    !>          If JOBZ = 'N' and N > 1, LWORK >= 2*N.
    !>          If JOBZ = 'V' and N > 1, LWORK >= 1 + 5*N + 2*N**2.
    !>
    !>          If LWORK = -1, then a workspace query is assumed; the routine
    !>          only calculates the optimal sizes of the WORK and IWORK
    !>          arrays, returns these values as the first entries of the WORK
    !>          and IWORK arrays, and no error message related to LWORK or
    !>          LIWORK is issued by XERBLA.
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
    !>          On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.
    !>

    LIWORK

    !>          LIWORK is INTEGER
    !>          The dimension of the array IWORK.
    !>          If JOBZ  = 'N' or N <= 1, LIWORK >= 1.
    !>          If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N.
    !>
    !>          If LIWORK = -1, then a workspace query is assumed; the
    !>          routine only calculates the optimal sizes of the WORK and
    !>          IWORK arrays, returns these values as the first entries of
    !>          the WORK and IWORK arrays, and no error message related to
    !>          LWORK or LIWORK is issued by XERBLA.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>          > 0:  if INFO = i, and i is:
    !>             <= N:  the algorithm failed to converge:
    !>                    i off-diagonal elements of an intermediate
    !>                    tridiagonal form did not converge to zero;
    !>             > N:   if INFO = N + i, for 1 <= i <= N, then DPBSTF
    !>                    returned INFO = i: B is not positive definite.
    !>                    The factorization of B could not be completed and
    !>                    no eigenvalues or eigenvectors were computed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line 219 of file dsbgvd.f.

Author

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